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180. Problem 2.40 (R) A stick at rest in S has a length L
and is inclined at angle
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to the
x-axis. We have to find its length
and
angle of inclination
to the
axis as
measured by an observer in
moving
with a speed v relative to x along the
axes.
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Solution: Click For PDF Version In the inertial frame S the rod is at rest. Its length measured in S is L. The x and y components of the length of the rod in frame S are
where as shown in the diagram the rod is inclined at angle
The inertial frame
By Lorentz transformations we note that
The length
And
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with respect to x-axis.
and
the inclination of the rod with respect to
axis be by
an angle
. Its
components
measured by
will
therefore be
